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Full text of "The scale of the universe"

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Vol. 2. Part 3 MAY, 1921 Number 11 

BULLETIN 

OF THE 

NATIONAL Research 
Council 



THE scale of the UNIVERSE 

By Harlow Shapley 
Mount Wilson Observatory, Carnegie Institution of Washington 

and 

Heber D. Curtis 

Director, Allegheny Observatory 



REPRINTED FOR NATURAL SCIENCES 9 
HARVARD UNIVERSITY 



Published by The National Research Council 

OP 

The National Academy op Sciences 

Washington, D. C. 

1921 



•if,i:/U- ^ ffA'^j-^^ 



BULLETIN 

OF THE 

NATIONAL RESEARCH COUNCIL 

Vol.2. Part 3 ^^^ • '^^' Number 11 



THE SCALE OF THE UNIVERSE* 

Part I 

By Harlow Shapley 

Mount Wilson Observatory, Carnegie Institution of Washington 

Part II 

By Heber D. Curtis 

Director, Allegheny Observatory 



CONTENTS 
Part I 

Evolution of the idea of galactic size I'l 

Surveying the solar neighborhood 176 

On the distances of globular clusters 180 

The dimensions and arrangement of the galactic system 191 

Part II 

Dimensions and structure of the galaxy 194 

Evidence furnished by the magnitude of the stars 198 

The spirals as external galaxies 210 

Part I 

By Harlow Shapley 

EVOLUTION OF THE IDEA OF GALACTIC SIZE 

The physical universe' was anthropocentric to primitive man. 
At a subsequent stage of intellectual progress it was centered in 
a restricted area on the surface of the earth. Still later, to Ptol- 
emy and his school, the universe w^as geocentric; but since the 

*This address and the following one by Dr. Heber D. Curtis are adapted from illus- 
trated lectures given on the William Ellery Hale Foundation before the National 
.\cademy of Sciences, April 26, 1920. The authors have exchanged papers in preparing 
them for publication in order that each might have the opportunity of considering the 
point of view of the other. 

'The word "universe" is used in this paper in the restricted sense, as applying to the 
total of sidereal systems now known to exist. 

171 



OB 

^7 7 

S fi 



1 7 2 THE SCALE OF THE UNI VERSE: H. SHAPLE Y AND H. D. CURTIS 

time of Copernicus the sun, as the dominating body of the solar 
system, has been considered to be at or near the center of the stel- 
lar realm. With the origin of each of these successive concep- 
tions, the system of stars has ever appeared larger than was 
thought before. Thus the significance of man and the earth in 
the sidereal scheme has dwindled with advancing knowledge of 
the physical world, and our conception of the dimensions of the 
discernible stellar universe has progressively changed. Is not fur- 
ther evolution of our ideas probable? In the face of great accu- 
mulations of new and relevant information can we firmly main- 
tain our old cosmic conceptions ? 

As a consequence of the exceptional growth and activity of the 
great observatories, with their powerful methods of analyzing 
stars and of sounding space, we have reached an epoch, I believe, 
when another advance is necessary ; our conception of the galactic 
system must be enlarged to keep in proper relationship the ob- 
jects our telescopes are finding; the solar system can no longer 
maintain a central position. Recent studies of clusters and re- 
lated subjects seem to me to leave no alternative to the belief that 
the galactic system is at least ten times greater in diameter — at 
least a thousand times greater in volume — than recently supposed. 

Dr. Curtis,^ on the other hand, maintains that the galactic sys- 
tem has the dimensions and arrangement formerly assigned it by 
students of sidereal structure — he supports the views held a decade 
or so ago by Newcomb, Charlier, Eddington, Hertzsprung, and 
other leaders in stellar astronomy. In contrast to my present 
estimate of a diameter of at least three hundred thousand light- 
years Curtis outlines his position as follows i^ 

As to the dimensions of the galaxy indicated by our Milky Way,till 
recently there has been a fair degree of uniformity in the estimates of those 
who have investigated the subject. Practically all have deduced diam- 
eters of from 7,000 to 30,000 light-years. I shall assume a maximum 
galactic diameter of 30,000 light-years as representing sufficiently well this 
older view to which I subscribe though this is pretty certainly too large. 

I think it should be pointed out that when Newcomb was writ- 
ing on the subject some twenty years ago, knowledge of those 
special factors that bear directly on the size of the universe was 
extremely fragmentary compared with our information of to-day. 

'See Part II of this article, by Heber D. Curtis. 

^Quoted from a manuscript copy of his Washington address. 



THE SCALE OF THE UNIVERSE: H. SHAPLEY AND H. D. CURTIS 173 

In 1900, for instance, the radial motions of about 300 stars were 
known; now we know the radial velocities of thousands. Accu- 
rate distances were then on record for possibly 150 of the brightest 
stars, and now for more than ten times as many. Spectra were 
then available for less than one-tenth of the stars for which we 
have the types to-day. Practically nothing was known at that 
time of the photometric and spectroscopic methods of determin- 
ing distance; nothing of the radial velocities of globular clusters 
or of spiral nebulae, or even of the phenomenon of star streaming. 

As a further indication of the importance of examining anew 
the evidence on the size of stellar systems, let us consider the great 
globular cluster in Hercules — a vast sidereal organization con- 
cerning which we had until recently but vague ideas. Due to 
extensive and varied researches, carried on during the last few 
years at Mount Wilson and elsewhere, we now know the posi- 
tions, magnitudes, and colors of all its brightest stars, and many 
relations between color, magnitude, distance from the center, and 
star density. We know some of these important correlations 
with greater certainty in the Hercules cluster than in the solar 
neighborhood. We now have the spectra of many of the indi- 
vidual stars, and the spectral type and radial velocity of the clus- 
ter as a whole. We know the types and periods of light variation 
of its variable stars, the colors and spectral types of these vari- 
ables, and something also of the absolute luminosity of the bright- 
est stars of the cluster from the appearance of their spectra. Is 
it surprising, therefore, that we venture to determine the distance 
of Messier 13 and similar systems with more confidence than was 
possible ten years ago when none of these facts was known, or 
even seriously considered in cosmic speculations? 

If he were writing now, with knowledge of these relevant devel- 
opments, I believe that Newcomb would not maintain his former 
view on the probable dimensions of the galactic system. 

For instance. Professor Kapteyn has found occasion, with the 
progress of his elaborate studies of laws of stellar luminosity and 
density, to indicate larger dimensions of the galaxy than formerly 
accepted. In a paper just appearing as Mount Wilson Contribu- 
tion, No. 188,^ he finds, as a result of the research extending over 
some 20 years, that the density of stars along the galactic plane 
is quite appreciable at a distance of 40,000 light-years — giving a 

^The Contribution is published jointly with Dr. van Rhijn. 



I 74 THE SCALE OF THE UNIVERSE: H. SHAPLE Y AND H. D. CURTIS 

diameter of the galactic system, exclusive of distant star clouds 
of the Milky Way, about three times the value Curtis admits as 
a maximum for the entire galaxy. Similarly Russell, Eddington, 
and, I believe, Hertzsprung, now subscribe to larger values of 
galactic dimensions; and Charlier, in a recent lecture before the 
Swedish Astronomical Association, has accepted the essential fea- 
tures of the larger galaxy, though formerly he identified the local 
system of B stars with the whole galactic system and obtained 
distances of the clusters and dimension of the galaxy only a hun- 
dredth as large as I derive. 



SURVEYING THE SOLAR NEIGHBORHOOD 

Let us first recall that the stellar universe, as we know it, ap- 
pears to be a very oblate spheroid or ellipsoid — a disk-shaped sys- 
tem composed mainly of stars and nebulae. The solar system is 
not far from the middle plane of this flattened organization which 
we call the galactic system. Looking away from the plane we 
see relatively few stars; looking along the plane, through a great 
depth of star-populated space, we see great numbers of sidereal 
objects constituting the band of light we call the Milky Way. 
The loosely organized star clusters, such as the Pleiades, the dif- 
fuse nebulae such as the great nebula of Orion, the planetary 
nebulae, of which the ring nebula in Lyra is a good example, the 
dark nebulosities — all these sidereal types appear to be a part of 
the great galactic system, and they lie almost exclusively along 
the plane of the Milky Way. The globular clusters, though not 
in the Milky Way, are also affiliated with the galactic system; the 
spiral nebulae appear to be distant objects mainly if not entirely 
outside the most populous parts of the galactic region. 

This conception of the galactic system, as a flattened, watch- 
shaped organization of stars and nebulae, with globular clusters 
and spiral nebulae as external objects, is pretty generally agreed 
upon by students of the subject ; but in the matter of the distances 
of the various sidereal objects — the size of the galactic system — 
there are, as suggested above, widely divergent opinions. We 
shall, therefore, first consider briefly the dimensions of that part 
of the stellar universe concerning which there is essential unanim- 
ity of opinion, and later discuss in more detail the larger field, 



THE SCALE OF THE UNI \ 'ERSE: H. SHA PLE Y A XD H. D. CURTIS 1 7 5 




Pig. 1.— The region of the Apennines on the surface of the moon as photographed 
with the 100-inch reflector. Photograph by F. G. Pease. 









4 



(A) 



o 



EARTH 



MOON 



Fig. 2.— a group of sun-spots first appearing in February 1920 and lasting for about 100 
days. The shaded and unshaded regions indicate magnetic polarities of opposite 
signs. Drawing by S. B. Nicholson. 



■ D 



Fig. 3.— Two successive photographs on the same plate of the diffuse nebula N. G. C. 
221, made with the 100-inch reflector to illustrate the possibility of greatly increasing 
the'photographic power of a large reflector through the use of accessory devices. The 
exposure time for the picture on the left was fifteen minutes; it was five minutes for 
the picture on the right, which was made with the aid of the photographic intensifier 
described in Proc. Nat. Acad. Set., 6, 127, 1920. In preparing the figure the two 
photographs were enlarged to the same scale. 



1 76 THE SCALE OF THE UNI VERSE: H. SHAPLE Y AND H. D. CURTIS 

where there appears to be a need for modification of the older 
conventional view. 

Possibly the most convenient way of illustrating the scale of the 
sidereal universe is in terms of our measuring rods, going from 
terrestrial units to those of stellar systems. On the earth's sur- 
face we express distances in units such as inches, feet, or miles. 
On the moon, as seen in the accompanying photograph made 
with the 100-inch reflector, the mile is still a usable measuring 
unit; a scale of 100 miles is indicated on the lunar scene. 

Our measuring scale must be greatly increased, however, when 
we consider the dimensions of a star — distances on the surface 
of our sun, for example. The large sun-spots shown in the illustra- 
tion cannot be measured conveniently in units appropriate to 
earthly distance — in fact, the whole earth itself is none too large. 
The unit for measuring the distances from the sun to its attendant 
planets, is, however, 12,000 times the diameter of the earth; it 
is the so-called astronom:'cal unit, the average distance from 
earth to sun. This unit, 93,000,000 miles in length, is ample for 
the distances of planets and comets. It would probably suffice 
to measure the distances of whatever planets and comets there may 
be in the vicinity of other stars; but it, in turn, becomes cumber- 
some in expressing the distances from one star, to another, for 
some of them are hundreds of millions, even a thousand million, 
astronomical units away. 

This leads us to abandon the astronomical unit and to introduce 
the light-year as a measure for sounding the depth of stellar space. 
The distance Hght travels in a year is something less than six 
million million miles. The distance from the earth to the sun is, 
in these units, eight light-minutes. The distance to the moon 
is 1.2 light-seconds. In some phases of our astronomical prob- 
lems (studying photographs of stellar spectra) we make direct 
microscopic measures of a ten-thousandth of an inch; and indi- 
rectly we measure changes in the wave-length of light a million 
times smaller than this ; in discussing the arrangement of globular 
clusters in space, we must measure a hundred thousand light- 
years. Expressing these large and small measures with reference 
to the velocity of light, we have an illustration of the scale of 
the astronomer's universe — his measures range from the trillionth 
of a biUionth part of one hght-second, to more than a thousand 



THE SCALE OF THE UNIVERSE: H. SHAPLEY AND H. D. CURTIS 177 

light-centuries. The ratio of the greatest measure to the small- 
est is as 10^3 to 1. 

It is to be noticed that light plays an all-important role in the 
study of the universe ; we know the physics and chemistry of stars 
only through their light, and their distance from us we express 
by means of the velocity of light. The light-year, moreover, has 
a double value in sidereal exploration; it is geometrical, as we have 
seen, and it is historical. It tells us not only how far away an 
object is, but also how long ago the light we examine was started 
on its way. You do not see the sun where it is, but where it was 
eight minutes ago. You do not see faint stars of the Milky Way 
as they are now, but more probably as they were when the pyra- 
mids of Egypt were being built; and the ancient Egyptians saw 
them as they were at a time still more remote. We are, there- 
fore, chronologically far behind events when we study conditions 
or dynamical behavior in remote stellar systems; the motions, 
light-emissions, and variations now investigated in the Hercules 
cluster are not contemporary, but, if my value of the distance is 
correct, they are the phenomena of 36,000 years ago. The great 
age of these incoming pulses of radiant energy is, however, no 
disadvantage; in fact, their antiquity has been turned to good 
purpose in testing the speed of stellar evolution, in indicating 
the enormous ages of stars, in suggesting the vast extent of the 
universe in time as well as in space. 

Taking the light-year as a satisfactory unit for expressing the 
dimensions of sidereal systems, let us consider the distances of 
neighboring stars and clusters, and briefly mention the methods 
of deducing their space positions. For nearby stellar objects we 
can make direct .trigonometric measures of distance (parallax), 
using the earth's orbit or the sun's path through space as a base 
line. For many of the more distant stars spectroscopic methods 
are available, using the appearance of the stellar spectra and the 
readily measurable apparent brightness of the stars. For certain 
types of stars, too distant for spectroscopic data, there is still a 
chance of obtaining the distance by means of the photometric 
method. This method is particularly suited to studies of globular 
clusters; it consists first in determining, by some means, the real 
luminosity of a star, that is, its so-called absolute magnitude, and 
second, in measuring its apparent magnitude. Obviously, if a 
star of known real brightness is moved away to greater and greater 



178 THE SCALE OF THE UNIVERSE: H. SHAPLEY AND H. D. CURTIS 

distances, its apparent brightness decreases; hence, for such stars 
of known absolute magnitude, it is possible, using a simple for- 
mula, to determine the distance by measuring the apparent 
magnitude. 

It appears, therefore, that although space can be explored for a 
distance of only a few hundred light-yeans by direct trigonometric 
methods, we are not forced, by our inability to measure still smaller 
angles, to extrapolate uncertainly or to make vague guesses rela- 
tive to farther regions of space, for the trigonometrically deter- 
mined distances can be used to calibrate the tools of newer and less 
restricted methods. For example, the trigonometric methods of 
measuring the distance to moon, sun, and nearer stars are deci- 
dedly indirect, compared with the linear measurement of distance 
on the surface of the earth, but they are not for that reason 
inexact or questionable in principle. The spectroscopic and 
photometric methods of measuring great stellar distance are also 
indirect, compared with the trigonometric measurement of small 
stellar distance, but they, too, are not for that reason unreliable 
or of doubtful value. These great distances are not extrapola- 
tions. For instance, in the spectroscopic method, the absolute 
magnitudes derived from trigonometrically measured distances 
are used to derive the curves relating spectral characteristics 
to absolute magnitude; and the spectroscopic parallaxes for 
individual stars (whether near or remote) are, almost without 
exception, interpolations. Thus the data for nearer stars are 
used for purposes of calibration, not as a basis for extrapolation. 

By one method or the other, the distances of nearly 3,000 indi- 
vidual stars in the solar neighborhood have now been determined; 
only a few are within ten light-years of the sun. At a distance 
of about 130 light-years we find the Hyades, the well known clus- 
ter of naked eye stars; at a distance of 600 light-years, according 
to Kapteyn's extensive investigations, we come to the group of 
blue stars in Orion — another physically-organized cluster com- 
posed of giants in luminosity. At distances comparable to the 
above values we also find the Scorpio-Centaurus group, the 
Pleiades, the Ursa Major system. 

These nearby clusters are specifically referred to for two reasons. 

In the first place I desire to point out the prevalence through- 
out all the galactic system of clusters of stars, variously organized 
as to stellar density and total stellar content. The gravitational 



THE SCALE OF THE UNIVERSE: H. SHAPLE Y AND H. D. CURTIS 1 79 

organization of stars is a fundamental feature in the universe — 
a double star is one aspect of a stellar cluster, a galactic system 
is another. We may indeed, trace the clustering motive from 
the richest of isolated globular clusters such as the system in 
Hercules, to the loosely organized nearby groups typified in the 
bright stars of Ursa Major. At one hundred times its present 
distance, the Orion cluster would look much like Messier 37 or 
Messier 1 1 : scores of telescopic clusters have the general form and 
star density of the Pleiades and the Hyades. The difference 
between bright and faint clusters of the galactic system naturally 
appears to be solely a matter of distance. 

In the second place I desire to emphasize the fact that the nearby 
stars we use as standards of luminosity, particularly the blue 
stars of spectral type B, are members of stellar clusters. Therein 
lies a most important point in the application of photometric 
methods. We might, perhaps, question the validity of compar- 
ing the isolated stars in the neighborhood of the sun with stars in 
a compact cluster; but the comparison of nearby cluster stars 
with remote cluster stars is entirely reasonable, since we are now 
so far from primitive anthropocentric notions that it is foolish 
to postulate that distance from the earth has anything to do with 
the intrinsic brightness of stars. 

ON THE DISTANCES OF GLOBULAR CLUSTERS 

\. As stated above, astronomers agree on the distances to the 
nearby stars and stellar groups — the scale of the part of the uni- 
verse that we may call the solar domain. But as yet there is 
lack of agreement relative to the distances of remote clusters, 
stars, and star clouds — the scale of the total galactic system. 
The disagreement in this last particular is not a small difference 
of a few percent, an argument on minor detail; it is a matter of 
a thousand percent or more. 

Curtis maintains that the dimensions I find for the galactic 
system should be divided by ten or more (see quotation on page 
172) ; therefore, that galactic size does not stand in the way of inter- 
preting spiral nebulae as comparable galaxies (a theory that he 
favors on other- grounds but considers incompatible with the 
larger values of galactic dimensions). In his Washington address, 



i8o THE SCALE OF THE UNIVERSE: H. SHAPLEY AND H. D. CURTIS 

however, he greatly simplified the present discussion by accepting 
the results of recent studies on the following significant points : 

Proposition A . — The globular clusters form a part of our galaxy ; 
therefore the size of the galactic system proper is most probably 
not less than the size of the subordinate system of globular clus- 
ters. 

Proposition B. — The distances derived at Mount Wilson for 
globular clusters relative to one another are essentially correct. 
This implies among other things that (1) absorption of light in 
space has not appreciably affected the results, and (2) the globu- 
lar clusters are much alike in structure and constitution, differing 
mainly in distance. (These relative values are based upon appar- 
ent diameters, integrated magnitudes, the magnitudes of indi- 
vidual giants or groups of giants, and Cepheid variables; Charlier 
has obtained much the same results from apparent diameters 
alone, and Lundmark frorti apparent diameters and integrated 
magnitudes.) 

Proposition C. — Stars in clusters and in distant parts of the 
Milky Way are not peculiar — that is, uniformity of conditions 
and of stellar phenomena naturally prevails throughout the galac- 
tic system. 

We also share the same opinion, I believe, on the following points : 

a. The galactic system is an extremely flattened stellar organi- 
zation, and the appearance of a Milky Way is partly due to the 
existence of distinct clouds of stars, and is partly the result of 
depth along the galactic plane. 

b. The spiral nebulae are mostly very distant objects, probably 
not physical members of our galactic system. 

c. If our galaxy approaches the larger order of dimensions, a 
serious difficulty at once arises for the theory that spirals are gal- 
axies of stars comparable in size with our own : it would be neces- 
sary to ascribe impossibly great magnitudes to the new stars that 
have appeared in the spiral nebulae. 

2. Through approximate agreement on the above points, the 
way is cleared so that the outstanding difference may be clearly 
stated: Curtis does not believe that the numerical value of the 
distance I derive for any globular cluster is of the right order of 
magnitude. 

3. The present problem may be narrowly restricted therefore, 
and may be formulated as follows: Show that any globular cluster 



THE SCA LEOF THE UNI VERSE: H. SHA PLEY AND H. D. CURTIS 1 8 1 



is approximately as distant as derived at Mount Wilson ; then the 
distance of other clusters will be approximately right (see Propo- 
sition B), the system of clusters and the galactic system will have 
dimensions of the order assigned (see Proposition A), and the 
"comparable galaxy" theory of spirals will have met with a seri- 
ous, though perhaps not insuperable difficulty. 

In other words, to maintain my position it will suffice to show 
that any one of the bright globular clusters has roughly the dis- 
tance in light-years given below, rather than a distance one tenth 
of this value or less ■} 



Cluster 


Distance in 


Mean photographic 


magnitude 


light-years 


of brightest 25 


stars 




Apparent 


Absolute 


Messier 13 


36,000 


13.75 


-1.5 


Messier 3 


45,000 


14.23 


-1.5 


Messier 5 


38,000 


13.97 


-1.4 


Omega Centauri 


21,000 


12 3: 


-1.8: 



Similarly it should suffice to show that the bright objects in clus- 
ters are giants (cf. last column above), rather than stars of solar 
luminosity. 

4. From observation we know that some or all of these four 
clusters contain : 

a. An interval of at least nine magnitudes (apparent and abso- 
lute) between the brightest and faintest stars. 

h. A range of color-index from —0.5 to +2.0, corresponding to 
the whole range of color commonly found among assemblages of 
stars. 

c. Stars of types B, A, F, G, K, M (from direct observations 
of spectra), and that these types are in sufficient agreement with the 
color classes to permit the use of the latter for ordinary statistical 
considerations where spectra are not yet known. 

d. Cepheid and cluster variables which are certainly analogous 
to galactic variables of the same types, in spectrum, color change, 
length of period, amount of light variation, and all characters of 
the light-curve. 

>In the final draft of the following paper Curtis has qualified his acceptance of the 
foregoing propositions in such a manner that in some numerical details the comparisons 
given below are no longer accurately applicable to his arguments; I believe, however, 
that the comparisons do correctly contrast the present view with that generally accepted 
& few years ago. 



i82 THE SCALE OF THE UNIVERSE: H. SHAPLEY AND H. D. CURTIS 



e. Irregular, red, small-range variables of the Alpha Orionis 
type, among the brightest stars of the cluster.- 

/. Many red and yellow stars of approximately the same magni- 
tude as the blue stars, in obvious agreement with the giant star 
phenomena of the galactic system, and clearly in disagreement 
with all we know of color and magnitude relations for dwarf stars. 

5. From these preliminary considerations we emphasize two 
special deductions : 

First, a globular cluster is a pretty complete "universe" by 
itself, with typical and representative stellar phenomena, includ- 
ing several classes of stars that in the solar neighborhood are recog- 
nized as giants in luminosity. 

Second, we are very fortunately situated for the study of distant 
clusters — outside rather than inside. Hence we obtain a compre- 
hensive dimensional view, we can determine relative real lumi- 
nosities in place of relative apparent luminosities, and we have the 
distinct advantage that the most luminous stars are easily isolated 
and the most easily studied. None of the brightest stars in a 
cluster escapes us. If giants or super-giants are there, they are 
necessarily the stars we study. We cannot deal legitimately 
with the average brightness of stars in globular clusters, because 
the faintest limits are apparently far beyond our present tele- 
scopic power. Our ordinary photographs record only the most 
powerful radiators — encompassing a range of but three or four 
magnitudes at the very top of the scale of absolute luminosity, 
whereas in the solar domain we have a known extreme range of 
20 magnitudes in absolute brightness, and a generally studied 
interval of twelve magnitudes or more. 

6. Let us now examine some of the conditions that would exist 
in the Hercules Cluster (Messier 13) on the basis of the two oppos- 
ing values for its distance : 



a. Mean absolute photographic mag- 

nitude of blue stars (C. I. <0.0) 

b. Maximum absolute photographic 

magnitudes of cluster stars 

c. Median absolute photovisual mag- 

nitude of long-period Cepheids 

d. Hypothetical annual proper motion 




3,600 light-years, 
or less 



-|-5, or fainter 

-(-3.2, or fainter 

-|-3, or fainter 
0.04, or greater 



THE SCALE OF THE UNIVERSE: H. SHAPLEY AND H. D. CURTIS 183 

a. The blue stars. — The colors of stars have long been recog- 
nized as characteristic of spectral types and as being of invaluable 
aid in the study of faint stars for .which spectroscopic observations 
are difficult or impossible. The color-index, as used at Mount 
Wilson, is the difference between the so-called photographic 
(pg) and photovisual (pv.) magnitudes — the difference between 
the brightness of objects in blue-violet and in yellow-green Hght. 
For a negative color-index (C. I. =pg. — pv.<0.0) the stars are 
called blue and the corresponding spectral type is B ; for yellow 
stars, like the sun (type G), the color-index is about +0.8 mag.; 
for redder stars (types K, M) the color-index exceeds a magnitude. 
An early result of the photographic study of Messier 13 at Mount 
Wilson was the discovery of large numbers of negative color-indi- 
ces. Similar results were later obtained in other globular and 
open clusters, and among the stars of the galactic clouds. Natur- 
ally these negative color-indices in clusters have been taken with- 
out question to indicate B-type stars — a supposition that has later 
been verified spectroscopically with the Mount Wilson reflectors. ^ 
The existence of 15th magnitude B-type stars in the Hercules 
cluster seems to answer decisively the question of its distance, 
because B stars in the solar neighborhood are invariably giants 
(more than a hundred times as bright as the sun, on the average), 
and such a giant star can appear to be of the fifteenth magnitude 
only if it is more than 30,000 light-years away. 

We have an abundance of material on distances and absolute 
magnitudes of the hundreds of neighboring B's — there are direct 
measures of distance, as well as mean distances determined from 
parallactic motions, from observed luminosity curves, from stream 
motions, and from radial velocities combined with proper motion. 
Russell, Plummer, CharHer, Eddington, Kapteyn, and others 
have worked on these stars with the universal result of finding 
them giants. 

Kapteyn's study of the B stars is one of the classics of modern 
stellar astronomy; his methods are mainly the well-tried methods 
generally used for studies of nearby stars. In his various lists of 
B's more than seventy percent are brighter than zero absolute 

'Adams and van Maanen published several years ago the radial velocities and spec- 
tral types of a number of B stars in the double cluster in Perseus, Ast. Jour., Albany 
N. Y., 27, 1913 (187-188). 



i84 THE SCALE OF THE UNIVERSE: H. SHAPLEY AND H. D. CURTIS 

photographic magnitude,' and only two out of 424 are fainter 
than +3. This result should be compared with the above-men- 
tioned requirement that the absolute magnitudes of the blue 
stars in Messier 13 should be +5 or fainter in the mean, if the 
distance of the cluster is 3,600 light-years or less, and no star in 
the cluster should be brighter than +3. • 

A question might be raised as to the completeness of the materi- 
al used by Kapteyn and others, for if only the apparently bright 
stars are studied, the mean absolute magnitudes may be too high. 
Kapteyn, however, entertains little doubt on this score, and an 
investigation- of the distribution of B-type stars, based on the 
Henry Draper Catalogue, shows that faint B's are not present in 
the Orion region studied by Kapteyn. 

The census in local clusters appears to be practically complete 
without revealing any B stars as faint as -f-5. But if the Hercules 
cluster were not more distant than 3,600 light-years, its B stars 
would be about as faint as the sun, and the admitted uniformity 
throughout the galactic system (Proposition C) would be gain- 
said : for although near the earth, whether in clusters or not, the B 
stars are giants, away from the earth in all directions, whether in 
the Milky Way clouds or in clusters, they would be dwarfs — and 
the anthropocentric theory could take heart again. 

Let us emphasize again that the near and the distant blue stars 
we are intercomparing are all cluster stars, and that there appears 
to be no marked break in the gradation of clusters, either in total 
content or in distance, from Orion through the faint open clusters 
to Messier 13. 

b. The maximum absolute magnitude of cluster stars. — In various 
nearby groups and clusters the maximum absolute photographic 
brightness, determined from direct measures of parallax or stream 
motion or from both, is known to exceed the following values: 

iStars of types B8 and B9 are customarily treated with the A type in statistical dis- 
cussion; even if they are included with the B's, 64 per cent of Kapteyn's absolute magni- 
tudes are brighter than zero and only 4 per cent are fainter than +2. No stars of types 
B8 or B9 fainter than +3 are in Kapteyn's Hsts. 

2Shapley, H., Proceedings Nat. Acad. Sci., 5, 1900 (434-440); a further treatment of 
this problem is to appear in a forthcoming Mount Wilson Contribution. 



THE SCALE OF THE UNIVERSE: H. SHAPLEY AND H. D. CURTIS iS- 





M 


Ursa Major system 


-1.0 


Moving cluster in Perseus 


-0 5 


Hyades 


+ 1.0 


Scorpio-Centaurus cluster 


-2.5 


Orion nebula cluster 


-2.5 


Ple-ades 


-10 


61 Cygni group^ 


+ 10 



No nearby physical group is known, with the possible excep- 
tion of the 61 Cygni drift, in which the brightest stars are fainter 
than +1.0. The mean M of the above list of clusters is —0.8; 
yet for all distant physical groups it must be +3 or fainter (not- 
withstanding the certain existence within them of Cepheid vari- 
ables and B-type stars), if the distance of Messier 13 is 3,600 light- 
years or less. Even if the distance is 8,000 light-years, as Curtis 
suggests in the following paper, the mean M would need to be 
-f 1 .4 or fainter — a value still irreconcilable with observations on 
nearby clusters. 

The requirement that the bright stars in a globular cluster 
should be in the maximum only two magnitudes brighter than 
our sun is equivalent to saying that in Messier 13 there is not 
one real giant among its thirty or more thousand stars. It is 
essentially equivalent, in view of Proposition B, to holding that 
of the two or three million stars in distant clusters (about half a 
million of these stars have been actually photographed) there is 
not one giant star brighter than absolute photographic magnitude 
+ 2. And we have just seen that direct measures show that all 
of our nearby clusters contain such giants; indeed some appear 
to be composed mainly of giants. 

As a further test of the distances of globular clusters, a special 
device has been used with the Hooker reflector. With a thin 
prism placed in the converging beam shortly before the focus, we 
may photograph for a star (or for each of a group of stars) a small 
spectrum that extends not only through the blue region ordinarily 
photographed, but also throughout the yellow and red. By using 
specially prepared photographic plates, sensitive in the blue and 
red but relatively insensitive in the green-yellow, the small spec- 
tra are divided in the middle, and the relative intensity of the blue 
and red parts depends, as is well known, on spectral type and 

iThe absolute visual magnitude of 6 Virginis (spectrum G6) is 0.0 according to the 
Mount Wilson spectroscopic paralla.\ kindly communicated by Mr. Adams. 



1 86 THE SCALE OF THE UNIVERSE: H. SHAPLEY AND H. D. CURTIS 

absolute magnitude; giants and dwarfs, of the same type in the 
Harvard system of spectral classification, show markedly different 
spectra. The spectral types of forty or fifty of the brighter stars 
in the Hercules cluster are known, classified as usual on the basis 
of spectral lines. Using the device described above, a number of 
these stars have been photographed side by side on the same plate 
with well known giants and dwarfs of the solar neighborhood for 
which distances and absolute magnitudes depend on direct mea- 
sures of parallax. On the basis of the smaller distance for Messier 
13, the spectra of these cluster stars (being then of absolute magni- 
tude fainter than -\-4) should resemble the spectra of the dwarfs. 
But the plates clearly show that in absolute brightness the cluster 
stars equal, and in many cases even exceed, the giants — a result 
to be expected if the distance is of the order of 36,000 light-years. 

The above procedure is a variation on the method used by 
Adams and his associates on brighter stars where sufficient dis- 
persion can be obtained to permit photometric intercomparison 
of sensitive spectral lines. So far as it has been applied to clus- 
ters, the usual spectroscopic method supports the above conclu- 
sion that the bright red and yellow stars in clusters are giants. 

An argument much insisted upon by Curtis is that the average 
absolute magnitude of stars around the sun is equal to or fainter 
than solar brightness, hence, that average stars we see in clusters 
are also dwarfs. Or, put in a different way, he argues that since 
the mean spectral class of a globular cluster is of solar type and 
the average solar-type star near the sun is of solar luminosity, the 
stars photographed in globular clusters must be of solar luminosity, 
hence not distant. This deduction, he holds, is in compliance 
with proposition C — uniformity throughout the universe. But 
in drawing the conclusions, Curtis apparently ignores, first, the 
very common existence of red and yellow giant stars in stellar 
systems, and second, the circumstance mentioned above in Section 
5 that in treating a distant external system we naturally first 
observe its giant stars. If the material is not mutually extensive 
in the solar domain and in the remote cluster (and it certainly is 
not for stars of all types) , then the comparison of averages means 
practically nothing because of the obvious and vital selection of 
brighter stars in the cluster. The comparison should be of nearby 
cluster with distant cluster, or of the luminosities of the same kinds 
of stars in the two places. 



THE SCALE OF THE UNIVERSE: H. SHAPLEY AND H. D. CURTIS 187 

Suppose that an observer, confined to a small area in a valley, 
attempts to measure the distances of surrounding mountain peaks. 
Because of the short base line allowed him, his trigonometric 
parallaxes are valueless except for the nearby hills. On the remote 
peaks, however, his telescope shows green foliage. First he as- 
sumes approximate botanical uniformity throughout all visible 
territory. Then he finds that the average height of all plants 
immediately around him (conifers, palms, asters, clovers, etc.) is 
one foot. Correlating this average with the measured angular 
height of plants visible against the sky-line on the distant peaks 
he obtains values of-the distances. If, however, he had compared 
the foliage on the nearby, trigonometrically-measured hills with 
that on the remote peaks, or had used some method of distinguish- 
ing various floral types, he would not have mistaken pines for 
asters and obtained erroneous results for the distances of the sur- 
rounding mountains. All the principles involved in the botanicaf 
parallax of a mountain peak have their analogues in the photo- 
metric parallax of a globular cluster. 

c. Cepheid variables. — Giant stars of another class, the Cepheid 
variables, have been used extensively in the exploration of globu- 
lar clusters. After determining the period of a Cepheid, its abso- 
lute magnitude is easily found from an observationally derived 
period-luminosity curve, and the distance of any cluster contain- 
ing such variables is determined as soon as the apparent magni- 
tudes are measured. Galactic Cepheids and cluster Cepheids are 
strictly comparable by Proposition C — a deduction that is amply 
supported by observations at Mount Wilson and Harvard, of color, 
spectrum, Hght curves, and the brightness relative to other types 
of stars. 

Curtis bases his strongest objections to the larger galaxy on 
the use I have made of the Cepheid variables, questioning the 
sufficiency of the data and the accuracy of the methods involved. 
But I beHeve that in the present issue there is Httle point in labor- 
ing over the details for Cepheids, for we are, if we choose, quah- 
tatively quite independent of them in determining the scale of 
the galactic system, and it is only qualitative results that are now 
at issue. We could discard the Cepheids altogether, use instead 
either the red giant stars and spectroscopic methods, or the hun- 
dreds of B-type stars upon which the most capable stellar astrono- 
mers have worked for years, and derive much the same distance 



i88 THE SCALE OF THE UNIVERSE: H. SHAPLEY AND H. D. CURTIS 

for the Hercules cluster, and for other clusters, and obtain conse- 
quently similar dimensions for the galactic system. In fact, the 
substantiating results from these other sources strongly fortify 
our belief in the assumptions and methods involved in the use of 
the Cepheid variables. 

Since the distances of clusters as given by Cepheid variables 
are qualitatively in excellent agreement with the distances as 
given by blue stars and by yellow and red giants, discussed in the 
foregoing sub-sections a and b, I shall here refer only briefly to 
four points bearing on the Cepheid problem, first noting that if 
the distances of clusters are to be divided by 10 or 15, the same 
divisor should be also used for the distances derived for galactic 
Cepheids. 

(1) The average absolute magnitude of typical Cepheids, ac- 
cording to my discussion of proper motions and magnitude corre- 
lations, is about —2.5. The material on proper motion has also 
been discussed independently by Russell, Hertzsprung, Kapteyn, 
Stromberg, and Scares; they all accept the validity of the method, 
and agree in making the mean absolute magnitude much the same 
as that which I derive. Scares finds, moreover, from a discussion 
of probable errors and of possible systematic errors, that the 
observed motions are irreconcilable with an absolute brightness 
five magnitudes fainter, because in that case the mean parallactic 
motion of the brighter Cepheids would be of the order of 0'.'160 
instead of "01 6±0"002 as observed. 

Both trigonometric and spectroscopic parallaxes of galactic 
Cepheids, as far as they have been determined, support the 
photometric values in demanding high luminosity ; the spectro- 
scopic and photometric methods are not wholly independent, how- 
ever, since the zero point depends in both cases on parallactic 
motion. 

(2) When parallactic motion is used to infer provisional abso- 
lute magnitudes for individual stars (a possible process only when 
peculiar motions are small and observations very good), the 
brighter galactic Cepheids indicate the correlation between lumi- 
nosity and period.' The necessity, how^ever, of neglecting indi- 
vidual peculiar motion and errors of observation for this proce- 

'Mr. Scares has called my attention to an error in plotting the provisional smoothed 
absolute magnitudes against log period for the Cepheids discussed in Mount Wilson 
Contribution No. 151. The preHminary curve for the galactic Cepheids is steeper than 
that fur the Small Magellanic Cloud, Omega Centauri, and other clusters. 



THE SCALE OF THE UNIVERSE: H. SHAPLEY AND H. D. CURTIS 189 

dure makes the correlation appear much less clearly for galactic 
Cepheids than for those of external systems (where proper motions 
are not concerned), and little importance could be attached to 
the period-luminosity curve if it were based on local Cepheids 
alone. When the additional data mentioned below are also treated 
in this manner, the correlation is practically obscured for galactic 
Cepheids, because of the larger observational errors. 

On account of the probably universal uniformity of Cepheid 
phenomena, however, we need to know only the mean parallactic 
motion of the galactic Cepheids to determine the zero point of 
the curve which is based on external Cepheids; and the individual 
motions do not enter the problem at all, except, as noted above, 
to indicate provisionally the existence of the period-luminosity 
relation. It is only this mean parallactic motion that other inves- 
tigators have used to show the exceedingly high luminosity of 
Cepheids. My adopted absolute magnitudes and distances for 
all these stars have been based upon the final period-luminosity 
curve, and not upon individual motions. 

(3) Through the kindness of Professor Boss and Mr. Roy of 
the Dudley Observatory, proper motions have been submitted for 
21 Cepheids in addition to the 13 in the Preliminary General 
Catalogue. The new material is of relatively low weight, but the 
unpublished discussion by Stromberg of that portion referring to 
the northern stars introduces no material alteration of the earlier 
result for the mean absolute brightness of Cepheids. 

It should be noted that the 18 pseudo-Cepheids discussed by 
Adams and Joy^ are without exception extremely bright (absolute 
magnitudes ranging from — 1 to — 4) ; they are thoroughly compar- 
able with the ordinary Cepheids in galactic distribution, spectral 
characteristics, and motion. 

(4) From unpublished results kindly communicated by van 
Maanen and by Adams, we have the following verification of the 
great distance and high luminosity of the important, high-velo- 
city, cluster-type Cepheid RR Lyrae: 

Photometric parallax 0.003 (Shapley) 

Trigonometric paralla.x -|-0. 006 ±0.006 (van Maanen) 

Spectroscopic parallax 0.004 (Adams, Joy, and Burwell) 

The large proper motion of this star, 0"25 annually, led Hertz- 

'Adams, W. S., and A. H. Joy, Publ. Ast. Soc. Pac, San Francisco, Calif., 31, 1919 
(184-186). 



I go THE SCALE OF THE UNIVERSE: H. SHAPLEY AND H. D. CURTIS 

sprung some years ago to suspect that the star is not distant, and 
that it and its numerous congeners in clusters are dwarfs. The 
large proper motion, however, indicates high real velocity rather 
than nearness, as the above results show. More recently Hertz- 
sprung has reconsidered the problem and, using the cluster vari- 
ables, has derived a distance of the globular cluster Messier 3 in 
essential agreement with my value. 

d. Hypothetical annual proper motion. — The absence of observed 
proper motion for distant clusters must be an indication of their 
great distance because of the known high velocities in the line of 
sight. The average radial velocity of the globular clusters appears 
to be about 150 km/sec. By assuming, as usual, a random distri- 
bution of velocities, the transverse motion of Messier 13 and sim- 
ilar bright globular clusters should be greater than the quite appre- 
ciable value of 0.04 a year if the distance is less than 3,600 
light-years. No proper motion has been found for distant clusters ; 
Lundmark has looked into this matter particularly for five systems 
and concludes that the annual proper motion is less than O'Ol. 

7. Let us summarize a few of the results of accepting the re- 
stricted scale of the galactic system. 

If the distances of globular clusters must be decreased to one- 
tenth, the light-emitting power of their stars can be only a hun- 
dredth that of local cluster stars of the same spectral and photo- 
metric types. As a consequence, I believe Russell's illuminative 
theory of spectral evolution would have to be largely abandoned, 
and Eddington's brilliant theory of gaseous giant stars would need 
to be greatly modified or given up entirely. Now both of these 
modern theories have their justification, first, in the fundamental 
nature of their concepts and postulates, and second, in their great 
success in fitting observational facts. 

Similarly, the period-luminosity law of Cepheid variation would 
be meaningless; Kapteyn's researches on the structure of the local 
cluster would need new interpretation, because his luminosity 
laws could be applied locally but not generally ; and a very serious 
loss to astronomy would be that of the generality of spectroscopic 
methods of determining star distances, for it would mean that 
identical spectral characteristics indicate stars differing in bright- 
ness by 100 to 1, depending only upon whether the star is in the 
solar neighborhood or in a distant cluster. 



THE SCALE OF THE UNIVERSE: H. SHAPLEY AND H. D. CURTIS igi 

THE DIMENSIONS AND ARRANGEMENT OF THE GALACTIC 

SYSTEM 

When we accept the view that the distance of the Hercules 
cluster is such that its stellar phenomena are harmonious with 
local stellar phenomena — its brightest stars typical giants, its 
Cepheids comparable with our own — then it follows that fainter, 
smaller, globular clusters are still more distant than 36,000 light- 
years. One-third of those now known are more distant than 
100,000 light-years; the most distant is more than 200,000 light- 
years away, and the diameter of the whole system of globular 
clusters is about 300,000 light-years. 

Since the affiliation of the globular clusters with the galaxy is 
shown by their concentration to the plane of the Milky Way and 
their symmetrical arrangement with respect to it, it also follows 
that the galactic system of stars is as large as this subordinate 
part. During the past year we have found Cepheid variables and 
other stars of high luminosity among the fifteenth magnitude 
stars of the galactic clouds; this can only mean that some parts 
of the clouds are more distant than the Hercules cluster. There 
seems to be good reason, therefore, to believe that the star-popu- 
lated regions of the galactic system extend at least as far as the 
globular clusters. 

One consequence of accepting the theory that clusters outline 
the form and extent of the galactic system, is that the sun is 
found to be very distant from the middle of the galaxy. It ap- 
pears that we are not far from the center of a large local cluster 
or cloud, but that cloud is at least 50,000 light-years from the 
galactic center. Twenty years ago Newcomb remarked that the 
sun appears to be in the galactic plane because the Milky Way 
is a great circle — an encircling band of light — and that the sun 
also appears near the center of the universe because the star 
density falls off with distance in all directions. But he concludes 
as follows : 

"Ptolemy showed by evidence, which, from his standpoint, looked as 
sound as that which we have cited, that the earth was fixed in the center 
of the universe. May we not be the victim of some fallacy, as he was?" 

Our present answer to Newcomb's question is that we have been 
victimized by restricted methods of measuring distance and by 
the chance position of the sun near the center of a subordinate 
system; w-e have been misled, by the consequent phenomena, into 



192 THE SCALE OF THE UNIVERSE: H. SHAPLEY AND II. D. CLRTIS 

thinking that we are in the midst of things. In much the same 
way ancient man was misled by the rotation of the earth, with 
the consequent apparent daily motion of all heavenly bodies 
around the earth, into believing that even his little planet was 
the center of the universe, and that his earthly gods created and 
judged the whole. 

If man had reached his present intellectual position in a later 
geological era, he might not have been led to these vain conceits 
concerning his position in the physical universe, for the solar sys- 
tem is rapidly receding from the galactic plane, and is moving 
away from the center of the local cluster. If that motion remains 
unaltered in direction and amount, in a hundred million years or 
so the Milky Way will be quite different from an encircling band 
of star clouds, the local cluster will be a distant object, and the 
star density will no longer decrease with distance from the sun 
in all directions. 

Another consequence of the conclusion that the galactic system 
is of the order of 300,000 light-years in greatest diameter, is the 
previously mentioned difficulty it gives to the "comparable- 
galaxy" theory of spiral nebulae. I shall not undertake a descrip- 
tion and discussion of this debatable problem. Since the theory 
probably stands or falls with the hypothesis of a small galactic 
system, there is little point in discussing other material on the 
subject, especially in view of the recently measured rotations of 
spiral nebulae which appear fatal to such an interpretation. 

It seems to me that the evidence, other than the admittedly 
critical tests depending on the size of the galaxy, is opposed to the 
view that the spirals are galaxies of stars comparable with our 
own. In fact, there appears as yet no reason for modifying the 
tentative hypothesis that the spirals are not composed of typical 
stars at all, but are truly nebulous objects. Three very recent 
results are, I believe, distinctly serious for the theory that spiral 
nebulae are comparable galaxies — (1) Scares' deduction that none 
of the known spiral nebulae has a surface brightness as small as 
that of our galaxy; (2) Reynold's study of the distribution of 
light and color in typical spirals, from which he concludes they 
cannot be stellar systems; and (3) van Maanen's recent measures 
of rotation in the spiral M 33, corroborating his earlier work on 
Messier 101 and 81, and indicating that these bright spirals cannot 



THE SCALE OF THE UNIVERSE: H. SHAPLEY AND H. D. CURTIS 193 

reasonably be the excessively distant objects required by the 
theory. 

But even if spirals fail as galactic systems, there may be else- 
where in space stellar systems equal to or greater than ours — as 
yet unrecognized and possibly quite beyond the power of existing 
optical devices and present measuring scales. The modern tele- 
scope, however, with such accessories as high-power spectroscopes 
and photographic intensifiers, is destined to extend the inquiries 
relative to the size of the universe much deeper into space, and 
contribute further to the problem of other galaxies. 



1 94 THE SCA LE OF THE UNI I 'ERSE: H. SHA PLE Y A ND H. D. CURTIS 

Part II 
Bv Heber D. Curtis 

DIMENSIONS AND STRUCTURE OF THE GALAXY 

Definition of units employed. — The distance traversed by light 
in one year, 9.5X10'- km., or nearly six trillion miles, known as 
the light-year, has been in use for about two centuries as a means 
of visualizing stellar distances, and forms a convenient and easily 
comprehended unit. Throughout this paper the distances of the 
stars will be expressed in light-years. 

The absolute magnitude of a star is frequently needed in order 
that we may compare the luminosities of different stars in terms 
of some common unit. It is that apparent magnitude which the 
star would have if viewed from the standard distance of 32.6 
light-years (corresponding to a parallax of OT). 

Knowing the parallax, or the distance, of a star, the absolute 
magnitude may be computed from one of the simple equations: 
Abs. Magn. =App. Magn.-|-5-f-5Xlog (parallax in seconds of arc) 
Abs. Magn.=App. Magn. -f 7. 6 — 5 X log (distance in light-years). 

Limitations in studies of galactic dimensions. — By direct meth- 
ods the distances of individual stars can be determined with con- 
siderable accuracy out to a distance of about two hundred light- 
years. 

At a distance of three hundred light-years (28X10^^ km.) the 
radius of the earth's orbit (1.5X10^ km.) subtends an angle sHghtly 
greater than 0"01, and the probable error of the best modern 
photographic parallax determinations has not yet been reduced 
materially below this value. The spectroscopic method of deter- 
mining stellar distances through the absolute magnitude probably 
has, at present, the same limitations as the trigonometric method 
upon which the spectroscopic method depends for its absolute scale. 

A number of indirect methods have been employed which ex- 
tend our reach into space somewhat farther for the average dis- 
tances of large groups or classes of stars, but give no information 
as to the individual distances of the stars of the group or class. 
Among such methods may be noted as most important the various 
correlations which have been made between the proper motions of 
the stars and the parallactic motion due to the speed of our sun 
in space, or between the proper motions and the radial velocities 
of the stars. 



THE SCALE OF THE UNIVERSE: H. SHAPLEY AND H. D. CURTIS 195 

The limitations of such methods of correlation depend, at pres- 
ent, upon the fact that accurate proper motions are known, in 
general, for the brighter stars only. A motion of 20 km/sec. 
across our line of sight will produce the following annual proper 
motions: 

Distance 100 1. y. 500 1. y. 1,000 1. y. 

Annual p. m. 0"14 0:03 O'Ol 

The average probable error of the proper motions of Boss is 
about 0"006. Such correlation methods are not, moreover, a 
simple matter of comparison of values, but are rendered difficult 
and to some extent uncertain by the puzzling complexities brought 
in by the variation of the space motions of the stars with spectral 
type, stellar mass (?), stellar luminosity (?), and still imperfectly 
known factors of community of star drift. 

It will then be evident that the base-line available in studies of 
the more distant regions of our galaxy is woefully short, and that 
in such studies we must depend largely upon investigations of the 
distribution and of the frequency of occurrence of stars of tl:ie dif- 
ferent apparent magnitudes and spectral types, on the assumption 
that the more distant stars, when taken in large numbers, will 
average about the same as known nearer stars. This assumption 
is a reasonable one, though not necessarily correct, as we have 
little certain knowledge of galactic regions as distant as five hun- 
dred light-years. 

Were all the stars of approximately the same absolute magni- 
tude, or if this were true even for the stars of any particular type 
or class, the problem of determining the general order of the dimen- 
sions of our galaxy would be comparatively easy. 

But the problem is complicated by the fact that, taking the 
stars of all spectral types together, the dispersion in absolute 
luminosity is very great. Even with the exclusion of a small 
number, of stars which are exceptionally bright or faint, this dis- 
persion probably reaches ten absolute magnitudes, which would 
correspond to a hundred-fold uncertainty in distance for a given 
star. However, it will be seen later that we possess moderately 
definite information as to the average absolute magnitude of the 
stars of the different spectral types. 

Dimensions of our galaxy. — Studies of the distribution of the 
stars and of the ratio between the numbers of stars of successive 



196 THE SCALE OF THE UNIVERSE: H. SHAPLEY A ND H. D. CURTIS 

apparent magnitudes have led a number of investigators to the 
postulation of fairly accordant dimensions for the galaxy ; a few may 
be quoted: 

Wolf; about 14,000 light-years in diameter. 
Eddington; about 15,000 light-years. 
Shapley (19 15); about 20,000 light-years, 

Newcomb; not less than 7,000 light-years; later — perhaps 30,000 light-years in diam- 
eter and 5,000 light-years in thickness. 
Kapteyn; about 60,000 light-years.' 

General structure of the galaxy. — From the lines of investigation 
mentioned above there has been a similar general accord in the 
deduced results as to the shape and structure of the galaxy: 

1. The stars are not infinite in number, nor uniform in distribution. 

2. Our galaxy, delimited for us by the projected contours of the Milky Way, con- 
tains possibly a billion suns. 

3. This galaxy is shaped much like a lens, or a thin watch, the thickness being prob- 
ably less than one-sixth of the diameter. 

4. Our Sun is located fairly close to the center of figure of the galaxy. 

5. The stars are not distributed uniformly through the galaxy. A large proportion 
are probably actually within the ring structure suggested by the appearance of the Milky 
Way, or are arranged in large and irregular regions of greater star density. The writer 
believes that the Milky Way is at least as much a structural as a depth eflfect. 

A spiral structure has been suggested for our galaxy; the evidence for such a spiral 
structure is not very strong, except as it may be supported by the analogy of the spirals 
as island universes, but such a structure is neither impossible nor improbable. The posi- 
tion of our Sun near the center of figure of the galaxy is not a favorable one for the 
precise determination of the actual galactic structure. 

Relative paucity of galactic genera. — Mere size does not neces- 
sarily involve complexity; it is a remarkable fact that in a galaxy 
of a thousand million objects we observe, not ten thousand differ- 
ent types, but perhaps not more than five main classes, outside 
the minor phenomena of our own solar system. 

1. The stars. — The first and most important class is formed by the stars. In accord- 
ance with the type of spectrum exhibited, we may divide the stars into some eight or 
ten main types ; even when we include the consecutive internal gradations within these 
spectral classes it is doubtful whether present methods will permit us to distinguish as 
many as a hundred separate subdivisions in all. Average space velocities vary from 
10 to 30 km/sec, there being a well-marked increase in average space velocity as one 
proceeds from the blue to the redder stars. 

2. The globular star dusters are greatly condensed aggregations of from ten thousand 

'A complete bibliography of the subject would fill many pages. Accordingly, refer- 
ences to authorities will in general be omitted. An excellent and nearly complete Hst 
of references may be found in Lundmark's paper, — "The Relations of the Globular 
Clusters and Spiral Nebulae to the Stellar System," in K. Svenska Vet. Handlingar, 
Bd. 60. No. 8, p. 71, 1920. 



THE SCALE OF THE UNIVERSE: H. SHAPLEY AND H. D. CURTIS 197 

to one hundred thousand stars. Perhaps one hundred are known. Though quite 
irregular in grouping, they are generally regarded as definitely galactic in distribution. 
Space velocities are of the order of 300 km/sec. 

3. The diffuse nebulae are enormous, tenuous, cloud-like masses; fairly numerous; 
always galactic in distribution. They frequently show a gaseous spectrum, though 
many agree approximately in spectrum with their involved stars. Space velocities are 
very low. 

4. The planetary nebulae are small, round or oval, and almost always with a central 
star. Fewer than one hundred and fifty are known. They are galactic in distribu- 
tion; spectrum is gaseous; space velocities are about 80 km/sec. 

5. The spirals. — Perhaps a million are within reach of large reflectors; the spectrum 
is generally like that of a star cluster. They are emphatically non-galactic in distribu- 
tion, grouped about the galactic poles, spiral in form. Space velocities are of the order 
of 1200 km/sec. 

Distribution of celestial genera. — With one, and only one, excep- 
tion, all known genera of celestial objects show such a distribu- 
tion with respect to the plane of our Milky Way, that there can 
be no reasonable doubt that all classes, save this one, are integral 
members of our galaxy. We see that all the stars, whether typical, 
binary, variable, or temporary, even the rarer types, show this 
unmistakable concentration toward the galactic plane. So also 
for the diffuse and the planetary nebulae and, though som'ewhat 
less definitely, for the globular star clusters. 

The one exception is formed by the spirals; grouped about the 
poles of our galaxy, they appear to abhor the regions of greatest 
star density. They seem clearly a class apart. Never found in 
our Milky Way, there is no other class of celestial objects with 
their distinctive characteristics of form, distribution, and velocity 
in space. 

The evidence at present available points strongly to the con- 
clusion that the spirals are individual galaxies, or island universes, 
comparable with our own galaxy in dimensions and in number 
of component units. While the island universe theory of the 
spirals is not a vital postulate in a theory of galactic dimensions, 
nevertheless, because of its indirect bearing on the question, the 
arguments in favor of the island universe hypothesis will be in- 
cluded with those which touch more directly on the probable 
dimensions of our own galaxy. 

Other theories of galactic dimensions. — From evidence to be re- 
ferred to later Dr. Shapley has deduced very great distances for 
the globular star clusters, and holds that our galaxy has a diam- 
eter comparable with the distances which he has derived for the 



iqS the scale of the UNIVERSE: H. SHAPLE Y AND H. D. CURTIS 

clusters, namely, — a galactic diameter of about 300,000 light- 
years, or at least ten times greater than formerly accepted. The 
postulates of the two theories may be outlined as follows: 

Present Theory Shapley's Theory 

Our galaxy is probably not more than The galaxy is approximately 300,000 

30,000 light-years in diameter, and per- light-years in diameter, and 30,000, or 

haps 5,000 light-years in thickness. more, light-years in thickness. 

The clusters, and all other types of The globular clusters are remote ob- 

celestial objects except the spirals, are jects, but a part of our own galaxy. The 

component parts of our own galactic mo.st distant cluster is placed about 

system. 220,000 light-years away. 

The spirals are a class apart, and not The spirals are probably of nebulous 

intra-galactic objects. As island uni- constitution, and possibly not members 

verses, of the same order of size as our of our own galaxy, driven away in some 

galaxy, they are distant from us 500,000 manner from the regions of greatest star 

to 10,000,000, or more, light-years. density. 

EVIDENCE FURNISHED BY THE MAGNITUDE OF THE STARS 

The ''average''' star. — It will be of advantage to consider the two 
theories of galactic dimensions from the standpoint of the average 
star. What is the "average" or most frequent type of star of 
our galaxy or of a globular star cluster, and if we can with some 
probability postulate such an average star, what bearing will the 
characteristics of such a star have upon the question of its average 
distance from us? 

No adequate evidence is available that the more distant stars 
of our galaxy are in any way essentially different from stars of 
known distance nearer to us. It would seem then that we may 
safely make such correlations between the nearer and the more 
distant stars, en masse. In such comparisons the limitations of 
spectral type must be observed as rigidly as possible, and results 
based upon small numbers of stars must be avoided, if possible. 

Many investigations, notably Shapley's studies of the colors of 
stars in the globular clusters, and Path's integrated spectra of 
these objects and of the Milky Way, indicate that the average 
star of a star cluster or of the Milky Way will, in the great major- 
ity of cases, be somewhat like our Sun in spectral type, i. e., such 
an average star will be, in general, between spectral types F 
and K. 

Characteristics of F-K type stars of known distance.— The dis- 
tances of stars of type F-K in our own neighborhood have been 
determined in greater number, perhaps, than for the stars of any 
other spectral type, so that the average absolute magnitude of 



THE SCA LEOF THE UNI VERSE: H. SHA PLE Y A ND H.D.C UR TIS 1 99 

stars of this type seems fairly well determined. There is every 
reason to believe, however, that our selection of stars of these or 
other types for direct distance determinations has not been a repre- 
sentative one. Our parallax programs have a tendency to select 
stars either of great luminosity or of great space velocity. 

Kapteyn's values for the average absolute magnitudes of the 
stars of the various spectral types are as follows: 



Fype 


Average 




Abs. Magn 


B5 


+ 1.6 


A5 


+3.4 


F5 


+ 7 


G5 


+ 10 


K5 


+ 13 


M 


+ 15 



The same investigator's most recent luminosity-frequency curve 
places the maximum of frequency of the stars in general, taking 
all the spectral types together, at absolute magnitude +7.7. 

A recent tabulation of about five hundred modern photograph- 
ically determined parallaxes places the average absolute magni- 
tude of stars of type F-K at about -}-4.5. 

The average absolute magnitude of five hundred stars of spec- 
tral types F to M is close to +4, as determined spectroscopically 
by Adams. 

It seems certain that the two last values of the average absolute 
magnitude are too low, that is, — indicate too high an average 
luminosity, due to the omission from our parallax programs of the 
intrinsically fainter stars. The absolute magnitudes of the dwarf 
stars are, in general, fairly accurately determined; the absolute 
magnitudes of many of the giant stars depend upon small and un- 
certain parallaxes. In view of these facts we may somewhat ten- 
tatively take the average absolute magnitude of F-K stars of 
known distance as not brighter than -f 6; some investigators would 
prefer a value of -f7 or +8. 

Comparison of Milky Way stars with the ''average" stars. — We 
may take, without serious error, the distances of 10,000 and 100,000 
light-years respectively, as representing the distance in the two 
theories from our point in space to the central line of the Milky 
Way structure. Then the following short table may be prepared : 



200 THE SCALE OF THE UNIVERSE: H. SHAPLE Y A ND H. D. CURTIS 



Apparent 


Corresponding absolute magnitudes for distances of, — 


magnitudes 


10,000 light-years 


100,000 light-years 


10 


-2.4 


-7.4 


12 


-0.4 


-5.4 


14 


+ 1.6 


-3.4 


16 


+3.6 


-1.4 


18 


+5.6 


+0.6 


20 


+7.6 


+2.6 



It will be seen from the above table that the stars of apparent 
magnitudes 16 to 20, observed in our Milky Way structure in 
such great numbers, and, from their spectrum, believed to be pre- 
dominantly F-K in type, are of essentially the same absolute 
luminosity as known nearer stars of these types, if assumed to be 
at the average distance of 10,000 light-years. The greater value 
postulated for the galactic dimensions requires, on the other hand, 
an enormous proportion of giant stars. 

Proportion of giant stars among stars of known distance. — All 
existing evidence indicates that the proportion of giant stars in a 
given region of space is very small. As fairly representative of 
several investigations we may quote Schouten's results, in which 
he derives an average stellar density of 166,000 stars in a cube 
500 light-years on a side, the distribution in absolute magnitude 
being as follows : 



Absolute magnitudes 


No. of stars 


Relative percentages 


—5 to —2 


17 


.01 


-2 to +1 


760 


.5 


+ 1 to +5 


26800 


16 


+5 to +10 


138600 


83 



Comparison of the stars of the globular clusters with the ''average'' 
star. — From a somewhat cursory study of the negatives of ten 
representative globular clusters I estimate the average apparent 
visual magnitude of all the stars in these clusters as in the neighbor- 
hood of the eighteenth. More powerful instruments may even- 
tually indicate a somewhat fainter mean value, but it does not 
seem probable that this value is as much as two magnitudes in 
error. We then have: 



THE SCALE OF THE UNIVERSE: H. SHAPLEY AND H. D. CURTIS 201 



Apparent magnitude of 


Corresponding absolute magnitudes if at distances of, — 


average cluster star 


10 000 light-years 


100,000 light-years 


18 


+5.6 


+0.6 



Here again we see that the average F-K star of a cluster, if 
assumed to be at a distance of 10,000 Hght-years, has an average 
luminosity about the same as that found for known nearer stars 
of this type. The greater average distance of 100,000 light-years 
requires a proportion of giant stars enormously greater than is 
found in those regions of our galaxy of which we have fairly defi- 
nite distance data. 

While it is not impossible that the clusters are exceptional 
regions of space and that, with a tremendous spatial concentration 
of suns, there exists also a unique concentration of giant stars, the 
hypothesis that cluster stars are, on the whole, like those of known 
distance seems inherently the more probable. 

It would appear, also, that galactic dimensions deduced from 
correlations between large numbers of what we may term average 
stars must take precedence over values found from small numbers 
of exceptional objects, and that, where deductions disagree, we 
have a right to demand that a theory of galactic dimensions based 
upon the exceptional object or class shall not fail to give an ade- 
quate explanation of the usual object or class. 

The evidence for greater galactic dimensions. — The arguments for 
a much larger diameter for our galaxy than that hitherto held, 
and the objections which have been raised against the island uni- 
verse theory of the spirals rest mainly upon the great distances 
which have been deduced for the (^lobular star clusters. 

I am unable to accept the thesis that the globular clusters are 
at distances of the order of 100,000 light-years, feeling that much 
more evidence is needed on this point before it will be justifiable 
to assurne that the cluster stars are predominatingly giants rather 
than average stars. I am also influenced, perhaps unduly, by 
certain fundamental uncertainties in the data employed. The 
limitations of space available for the publication of this portion 
of the discussion unfortunately prevents a full treatment of the 
evidence. In calling attention to some of the uncertainties in 
the basal data, I must disclaim any spirit of captious criticism, 
and take this occasion to express my respect for Dr. Shapley's 



202 THE SCALE OF THE UNIVERSE: H. SHAPLE Y AND H. D. CURTIS 

point of view, and my high appreciation of the extremely valua- 
ble work which he has done on the clusters. I am willing to accept 
correlations between large masses of stellar data, whether of mag- 
nitudes, radial velocities, or proper motions, but I feel that the 
dispersion in stellar characteristics is too large to permit the use 
of limited amounts of any sort of data, particularly when such 
data is of the same order as the probable errors of the methods of 
observation. 

The deductions as to the very great distances of the globular 
clusters rest, in the final analysis, upon three lines of evidence: 

1. Determination of the relative distances of the clusters on the assumption that 
they are objects of the same order of actual size. 

2. Determination of the absolute distances of the clusters through correlations be- 
tween Cepheid variable stars in the clusters and in our galaxy. 

3. Determination of the absolute distances of the clusters through a comparison of 
their brightest stars with the intrinsically brightest stars of our galaxy. 

Of these three methods, the second is given most weight by 
Shapley. 

It seems reasonable to assume that the globular clusters are of 
the same order of actual size, and that from their apparent diam- 
eters the relative distances may be determined. The writer would 
not, however, place undue emphasis upon this relation. There 
would seem to be no good reason why there may not exist among 
these objects a reasonable amount of difference in actual size, 
say from thjee- to five-fold, differences which would not prevent 
them being regarded as of the same order of size, but which would 
introduce considerable uncertainty into the estimates of relative 
distance. 

The evidence from the Cepheid variable stars. — This portion of 
Shapley's theory rests upon the following three hypotheses or 
lines of evidence : 

A. That there is a close coordination between absolute magnitude and length of period 
for the Cepheid variables of our galaxy, similar to the relation discovered by Miss Lea- 
vitt among Cepheids of the ^Smaller Magellanic Cloud. 

B. That, if of identical periods, Cepheids anywhere in the universe have identical 
absolute magnitudes. 

C. This coordination of absolute magnitude and length of period for galactic Cepheids, 
the derivation of the absolute scale for their distances and the distances of the clusters, 
and, combined with A) and B), the deductions therefrom as to the much greater dimen- 
sions for our galaxy, depend almost entirely upon the sizes and the internal relationships 
of the proper motions of eleven Cepheid variables. 



THE SCALE OF THE i'MVEKSE: H. SIIAPLE Y A \D 11. P. CCKTIS 203 

Under the first heading, it will be seen later that the actual evi- 
dence for such a coordination among galactic Cepheids is very 
weak. Provided that the Smaller Magellanic Cloud is not in some 
way a unique region of space, the behavior of the Cepheid variables 
in this Cloud is, through analogy, perhaps the strongest argument 
for postulating a similar phenomenon among the Cepheid variables 
of our galaxy. 

Unfortunately there is a large dispersion in practically all the 
characteristics of the stars. That the Cepheids lack a reasonable 
amount of such dispersion is contrary to all experience for the 
stars in general. There are many who will regard the assumption 
made under B) above as a rather drastic one. 

If we tabulate the proper motions of these eleven Cepheids, as 
given by Boss, and their probable errors as well, it will be seen 
that the average proper motion of these eleven stars is of the 
order of one second of arc per century in either coordinate; that 
the average probable error is nearly half this amount, and that the 
probable errors of half of these twenty-two coordinates may well 
be described as of the same size as the corresponding -proper 
motions. 

Illustrations bearing on the uncertainty of proper motions of 
the order of O'Ol per year might be multiplied at great length. 
The fundamental and unavoidable errors in our star positions, the 
probable errors of meridian observations, the uncertainty in the 
adopted value of tlid^ constant of precession, the uncertainties 
introduced by the systematic corrections applied to different cata- 
logues, all have comparatively little effect when use is made of 
proper motions as large as ten seconds of arc per century. Proper 
motions as small as one second of arc per century are, however, still 
highly uncertain quantities, entirely aside from the question of 
the possible existence of systematic errors. As an illustration of 
the differences in such minute proper motions as derived by various 
authorities, the proper motions of three of the best determined of 
this list of eleven Cepheids, as determined by Auwers, are in dif- 
ferent quadrants from those derived by Boss. 

There seems no good reason why the smaller coordinates of this 
list of twenty-two ma}- not eventually prove to be different by 
once or twice their present magnitude, with occasional changes 
of sign. So small an amount of presumably uncertain data is 



204 THE SCALE OF THE UNI VERSE: H. SHAPLE Y AND H. D. CURTIS 

insufficient to determine the scale of our galaxy, and many will 
prefer to wait for additional material before accepting such evi- 
dence as conclusive. 
In view of: 

1. The known uncertainties of small proper motions, and, 

2. The known magnitude of the purely random motions of the 
stars, the determination of individual parallaxes from individual 
proper motions can never give results of value, though the average 
distances secured by such methods of correlation from large num- 
bers of stars are apparently trustworthy. The method can not 
be regarded as a valid one, and this applies whether the proper 
motions are very small or are of appreciable size. 

As far as the galactic Cepheids are concerned, Shapley's curve 
of coordination between absolute magnitude and length of period, 
though found through the mean absolute magnitude of the group 
of eleven, rests in reality upon individual parallaxes determined 
from individual proper motions, as may be verified by comparing 
his values for the parallax of these eleven stars with^ the values 
found directly from the upsilon component of the proper motion 
(namely, — that component which is parallel to the Sun's motion) 
and the solar motion. The differences in the two sets of values, 
0"0002 in the mean, arise from the rather elaborate system of 
weighting employed. 

The final test of a functional relation is the agreement obtained 
when applied to similar data not originally employed in deducing 
the relation. We must be ready to^allow some measure of devi- 
ation in such a test, but when a considerable proportion of other 
available data fails to agree within a reasonable amount, we shall 
be justified in withholding our decision. 

If the curve of correlation deduced by Shapley for galactic 
Cepheids is correct in both its absolute and relative scale, and if 
it is possible to determine individual distances from individual 
proper motions, the curve of correlation, using the same method 
as far as the proper motions are concerned (the validity of which 
I do not admit), should fit fairly well with other available proper 
motion and parallax data. The directly determined parallaxes 
are known for five of this group of eleven, and for five other 
Cepheids. There are, in addition, twenty-six other Cepheids or 
which proper motions have been determined. One of these was 

^Mt. Wilson Conlr. Xo. 151, Table V. 



THE SCALE OF THE UNIVERSE: H. SHAPLEY AND H. D. CURTIS 205 



Logarithm of the period 
+1.3 +1.4 +1.0 +0.5 +0.2 -0.2 -0.6 



\0 <^ 

\ 

\ 


Of 


^0# 


■ 

> 








\ 


\ Q 


) 










\ 


















:< 


) 























^ 




2) ^ 


^^ 


-- 




• • 




• i 




• 

b 

• 




• 






00 









k 



o 



* 2 

Fig. 1. — Agreement of other data with the luminosity-period correlation curve. Absolute 
magnitudes calculated from the upsilon component of the proper motion are indicated 
by circles; the eleven employed by Shapleyare marked with a bar. Black dots represent 
directly determined parallaxes. The arrows attached to the circles at the upper edge of 
the diagram indicate that either the parallax or the upsilon component of the proper 
motion is negative, and the absolute magnitude indeterminate in consequence. 

omitted by Shapley because of irregularity of period, one for 
irregularity of the light curve, two because the proper motions 
were deemed of insufficient accuracy, two because the proper 
motions are anomalously large; the proper motions of the others 
have been recently investigated at the Dudley Observatory, but 
have less weight than those of the eleven Cepheids used by 
Shapley. 



2o6 THE SCALE OF THE UNIVERSE: H. SHAPLEY AND H. D. CURTIS 

In Figure 1 the absolute magnitudes are plotted against the 
logarithm of the period; the curve is taken from Mt. Wilson 
Contr. No. 151, and is that finally adopted by Shapley after the 
introduction of about twelve Cepheids of long period in clusters, 
twenty-five from the Smaller Magellanic Cloud, and a large num- 
ber of short period cluster-type variables in clusters with periods 
less than a day, which have little effect on the general shape of 
the curve. The barred circles represent the eleven galactic 
Cepheids employed by Shapley, the black dots those Cepheids 
for which parallaxes have been determined, while the open circles 
indicate variables for which proper motions have since become 
available, or not employed originally by Shapley. For the stars 
at the upper edge of the diagram, the attached arrows indicate 
that either the parallax, or the upsilon component of the proper 
motion is negative, so that the absolute magnitude is indeter- 
minate, and may be anything from infinity -down. 

From the above it would seem that available observational data 
lend little support Ho the fact of a period-luminosity relation 
among galactic Cepheids. In view of the large discrepancies 
shown by other members of the group when plotted on this curve, 
it would seem wiser to wait for additional evidence as to proper 
motion, radial velocity, and, if possible, parallax, before entire 
confidence can be placed in the hypothesis that the Cepheids and 
cluster-type variables are invariably super-giants in absolute 
luminosity. 

Argument from the intrinsically brightest stars. — If the luminosity- 
frequency law is the same for the stars of the globular clusters as 
for our galaxy, it should be possible to correlate the intrinsically 
brightest stars of both regions and thus determine cluster dis- 
tances. It would seem, a priori, that the brighter stars of the 
clusters must be giants, or at least approach that type, if the stars 
of the clusters are like the general run of stars. Through the 
application of a spectroscopic method Shapley has found that 
the spectra of the brighter stars in clusters resemble the spectra of 
galactic giant stars, a method which should be exceedingly useful 
after sufficient tests have been made to make sure that in this 
phenomenon, as is unfortunately the case in practically all stellar 
characteristics, there is not a large dispersion, and also whether 
sHght differences in spectral type may at all materially affect the 
deductions. 



THE SCALE OF THE UNIVERSE: H. SHAPLEV AND H. D. CURTIS 207 

The average ''giant'' star. — Determining the distance of Messier 
3 from the variable stars which it contains, Shapley then derives 
absolute magnitude —1.5 as the mean luminosity of the twenty- 
five brightest stars in this cluster. From this mean value, —1.5, 
he then determines the distances of other clusters. Instead, how- 
ever, of determining cluster distances of the order of 100, 000 light- 
years by means of correlations on a limited number of Cepheid 
variables, a small and possibly exceptional class, and from the 
distances thus derived deducing that the absolute magnitudes of 
many of the brighter stars in the clusters are as great as —3, 
while a large proportion are greater than — 1, it would seem pref- 
erable to begin the line of reasoning with the attributes of known 
stars in our neighborhood, and to proceed from them to the clusters. 

What is the average absolute magnitude of a galactic giant star? 
On this point there is room for honest differe/nce of opinion, and 
there will doubtless be many who will regard the conclusions of 
this paper as ultra conservative. Confining ourselves to existing 
observational data, there is no evidence that a group of galactic 
giants, of average spectral type about G5, will have a mean abso- 
lute magnitude as great as —1.5; it is more probably in the 
neighborhood of +1-5, or three absolute magnitudes fainter, 
making Shapley's distances four times too large. 

Russell's suggestion is worth quoting in this connection, writ- 
ten in 1913, when parallax data were far more limited and less 
reliable than at present: 

The giant stars of all the .spectral classes appear to be of about the same 
mean brightness, — averaging a little above absolute magnitude zero, that 
is, about a hundred times as bright as the Sun. vSince the stars of this 
series . have been .selected by apparent brightness, which gives a 

strong preference to those of greatest luminosity, the average brightness 
of all the giant stars in a given region of space must be less than this, 
perhaps considerably so. 

Some reference has already been made to the doubtful value of 
parallaxes of the order of O'OIO, and it is upon such small or 
negative parallaxes that most of the very great absolute luminosi- 
ties in present lists depend. It seems clear that parallax work 
should aim at using as faint comparison stars as possible, and 
that the corrections applied to reduce relative parallaxes to abso- 
lute parallaxes should be increased very considerably over what 
was thought acceptable ten years ago. 



2o8 THE SCA LE OF THE UNI VERSE: H. SHAPLE Y A ND H. D. CUR TIS 

Frcm a study of the plotted absolute magnitudes by spectral 
type of about five hundred modern direct parallaxes, with due 
regard to the uncertainties of minute parallaxes, and keeping in 
mind that most of the giants will be of types F to M, there seems 
little reason for placing the average absolute magnitude of such 
giant stars as brighter than +2. 

The average absolute magnitude for the giants in Adams's list 
of five hundred spectroscopic parallaxes is +1.1. The two methods 
differ most in the stars of type G, where the spectroscopic method 
shows a maximum at +0.6, which is not very evident in the trigo- 
nometric parallaxes. 

In such moving star clusters as the Hyades group, we have 
thus far evidently observed only the giant stars of such groups. 

The mean absolute magnitude of forty-four stars believed to 
belong to the Hyades moving cluster is +2.3. The mean absolute 
magnitude of the thirteen stars of types F, G, and K, is +2.4 
The mean absolute magnitude of the six brightest stars is +0.8 
(two A5, one G, and three of K type). 

The Pleiades can not fittingly be compared with such clusters 
or the globular clusters; its composition appears entirely different 
as the brightest stars average about B5, and only among the faint- 
est stars of the cluster are there any as late as F in type. The 
parallax of this group is still highly uncertain. With Schouten's 
value of 0'.'037 the mean absolute magnitude of the six brightest 
stars is +1.6. 

With due allowance for the redness of the giants in clusters, 
Shapley's mean visual magnitude of the twenty-five brightest 
stars in twenty-eight globular clusters is about 14.5. Then, from 
the equation given in the first section of this paper we have, — 

+ 2 = 14.5 + 7.6 — 5Xlog distance, 
or, log distance = 4.02 = 10,500 light-years as the average distance. 

If we adopt instead the mean value of Adams +1.1, the distance 
becomes 17,800 light-years. 

Either value for the average distance of the clusters may be 
regarded as satisfactorily close to those postulated for a galaxy 
of the smaller dimensions held in this paper, in view of the many 
uncertainties in the data. Either value, also, will give on the 
same assumptions a distance of the order of 30,000 light-years 
for a few of the faintest and apparently most distant clusters. 
I consider it very doubtful whether any cluster is really so distant 



THE SCALE OF THE UNIVERSE: H. SHAPLEY AND H. D. CURTIS 



!09 



as this, but find no difficulty in provisionally accepting it as a 
possibility, without thereby necessarily extending the main struc- 
ture of the galaxy to such dimensions. While the clusters seem 
concentrated toward our galactic plane, their distribution in longi- 
tude is a most irregular one, nearly all lying in the quadrant between 
270^ and 0°. If the spirals are galaxies of stars, their analogy 
\YOuld explain the existence of frequent nodules of condensation 
(globular clusters?) lying well outside of and distinct from the 
main structure of a galaxy. 

It must be admitted that the B-type stars furnish something 
of a dilemma in any attempt to utilize them in determining cluster 
distances. 

From the minuteness of their proper motions, most investigators 
have deduced very great luminosities for such stars in our galaxy. 
Examining Kapteyn's values for stars of this type, it will be seen 
that he finds a range in absolute magnitude from +3.25 to —5.47. 
Dividing the 433 stars of his lists into two magnitude groups, we 
have: 

Mean abs. magn. 249 B stars, 

brighter than abs. magn. =—1.32 

Mean abs. magn. 184 B stars, 

fainter than abs. magn. = +0.99 

Mean abs. magn. all = — 0.36 

Either the value for the brighter stars, —1.32, or the mean of 
all, —0.36, is over a magnitude brighter than the average absolute 
magnitude of the giants of the other spectral types among nearer 
galactic stars. 

Now this galactic relation is apparently reversed in such clusters 
as M. 3 or M. 13, where the B-type stars are about three magni- 
tudes fainter than the brighter K and M stars and about a mag- 
nitude fainter than those of G type. Supposing that the present 
very high values for the galactic B-type stars are correct, if we 
assume similar luminosity for those in the clusters we must 
assign absolute magnitudes of —3 to —6 to the F to M stars of 
the clusters, for which we have no certain galactic parallel, with 
a distance of perhaps 100,000 light-years. On the other hand, if 
the F to M stars of the cluster are like the brighter stars of these 
types in the galaxy, the average absolute magnitude of the B-type 
stars will be only about +3, and too low to agree with present 



2 1 o THE SCA LEOF THE UNI VERSE: H. SHA PLE Y AND H. D. CUR TIS 

values for galactic B stars. I prefer to accept the latter alterna- 
tive in this dilemma, and to believe that there may exist B-type 
stars of only two to five times the brightness of the Sun. 

While I hold to a theory of galactic dimensions approximately 
one-tenth of that supported by Shapley, it does not follow that 
I maintain this ratio for any particular cluster distance. All that 
I have tried to do is to show that 10,000 light-years is a reason- 
able average cluster distance. 

There are so many assumptions and uncertainties involved that 
I am most hesitant in attempting to assign a given distance to a 
given cluster, a hesitancy which is not diminished by a consider- 
ation of the following estimates of the distance of M. 13 (The 
Great Cluster in Hercules). 

Shapley, 1915, provisional 100,000 light-years 

Charlier, 1916 170 Hght-years 

Shapley, 1917 36,000 light-years 

Schouten, 1918 4,300 hght-years 

Lundmark, 1920 21,700 light-years 

It should be stated here that Shapley's earlier estimate was 
merely a provisional assumption for computational illustration, 
but all are based on modern material, and illustrate the fact that 
good evidence may frequently be interpreted in different ways. 

My own estimate, based on the general considerations outlined 
earlier in this paper, would be about 8,000 light-years, and it 
would appear to me, at present, that this estimate is perhaps 
within fifty per cent of the truth. 

THE SPIRALS AS EXTERNAL GALAXIES 

The spirals. — If the spirals are island universes it would seem 
reasonable and most probable to assign to them dimensions of the 
same order as our galaxy. If, however, their dimensions are as 
great as 300,000 light-years, the island universes must be placed 
at such enormous distances that it would be necessary to assign 
what seem impossibly great absolute magnitudes to the novae 
which have appeared in these objects. For this reason the island 
universe theory has an indirect bearing on the general subject of 
galactic dimensions, though it is, of course, entirely possible to 
hold both to the island universe theory and to the belief in the 



THE SCALE OF THE UNI VERSE: H. SHAPLE Y A ND H. D. CURTIS 2 1 1 

greater dimensions for our galaxy by making the not improbable 
assumption that our own island universe, by chance, happens to 
be several fold larger than the average. 

Some of the arguments against the island universe theory of 
the spirals have been cogently put by Shapley, and will be quoted 
here for reference. It is only fair to state that these earlier state- 
ments do not adequately represent Shapley's present point of view, 
which coincides somewhat more closely with that held by the 
writer. 

With the plan of the sidereal system here outlined, it appears unlikely 
that the spiral nebulae can be considered separate galaxies of stars. In 
addition to the evidence heretofore existing, the following points seem 
opposed to the "island universe" theory: (a) the dynamical character of 
the region of avoidance; (b) the size of the galaxy; (c) the maximum 
luminosity attainable by a star; (d) the increasing commonness of high 
velocities among other sidereal objects, particularly those outside the 
region of avoidance . . . the cluster work strongly suggests the hypo- 
thesis that spiral nebulae . . . are, however, members of the galactic 
organization . . the novae in spirals may be considered as the en- 

gulfing of a star by the rapidly moving nebulosity. (Publ. Astron. Soc. 
of the Pacific, Feb. 1918, p. 53.) 

The recent work on star clusters, in so far as it throws some light on the 
probable extent and structure of the galactic system, justifies a brief recon- 
sideration of the question of external galaxies, and apparently leads to 
the rejection of the hypothesis that spiral nebulae should be interpreted 
as separate stellar systems. 

Let us abandon the comparison with the galaxy and assume an average 
distance for the brighter spirals that will give a reasonable maximum abso- 
lute magnitude for the novae (and in a footnote; — provisionally, let us 
say, of the order of 20,000 light-years). Further, it is possible to explain 
the peculiar distribution of the spirals and their systematic recession by 
supposing them repelled in some manner from the galactic system, which 
appears to move as a whole through a nebular field of indefinite extent. 
But the possibility of these hypotheses is of course not proposed as compe- 
tent evidence against the "island universe" theory. . . . Observa- 
tion and discussion of the radial velocities, internal motions, and distri- 
bution of the spiral nebulae, of the real and apparent brightness of novae, 
of the maximum luminosity of galactic and cluster stars, and finally of the 
dimensions of our own galactic system, all seem definitely to oppose the 
"island universe" hypothesis of the spiral nebulae. . . . [Publ. 
Astron. Soc. of the Pacific, Oct. 1919, pp. 261 ff.) 



2 1 2 THE SCALE OF THE UNIVERSE: H. SHAPLE Y A ND H. D. CURTIS 



The dilemma of the apparent dimensions of the spirals. — ^In appar- 
ent size the spirals range from a diameter of 2° (Andromeda), to 
minute flecks 5 ", or less, in diameter. 

They may possibly vary in actual size, roughly in the progres- 
sion exhibited by their apparent dimensions. 

The general principle of approximate equality of size for celes- 
tial objects of the same class seems, however, inherently the more 
probable, and has been used in numerous modern investigations, 
e. g., by Shapley in determining the relative distances of the clusters. 

On this principle of approximate equality of actual size: 



As Island Universes 

Their probable distances range from 
about 500,000 light-years (Andromeda), 
to distances of the order of 100,000,000 
light-years. 

At 500,000 light-years the Nebula of 
Andromeda would be 17,000 light-years 
in diameter, or of the same order of size 
as our galaxy. 



The spectrum of the spirals. — 

As Island Universes 

The spectrum of the average spiral is 
indistinguishable from that given by a 
star cluster. 

It is approximately F-G in type, and 
in general character resembles closely the 
integrated spectrum of our Milky Way. 

It is just such a spectrum as would be 
expected from a vast congeries of stars. 

The spectrum of the spirals offers no 
difficulties on the island universe theory. 



As Galactic Phenomena 
If the Nebula of Andromeda is but 
20,000 light-years distant, the minute 
spirals would need to be at distances of 
the order of 10,000,000 light-years, or far 
outside the greater dimensions postulated 
for the galaxy. 

If all are galactic objects, equality of 
size must be abandoned, and the minute 
spirals assumed to be about a thousand- 
fold smaller than the largest. 



As Galactic Phenomena 

If the spirals are intragalactic, we must 
assume that they are some sort of finely 
divided matter, or of gaseous constitu- 
tion. 

In either case we have no adequate and 
actually existing evidence by which we 
may explain their spectrum. 

Many diffuse nebulosities of our galaxy 
show a bright-line gaseous spectrum. 
Others, associated with bright stars, agree 
with their involved stars in spectrum, 
and are well explained as a reflection or 
resonance effect. 

Such an explanation seems untenable 
for most of the spirals. 



The distribution of the spirals. — The spirals are found in greatest 
numbers just where the stars are fewest (at the galactic poles), 
and not at all where the stars are most numerous (in the galactic 
plane). This fact makes it difficult, if not impossible, to fit the 
spirals into any coherent scheme of stellar evolution, either as a 
point of origin, or as a final evolutionary product. No spiral has 
as yet been found actually within the structure of the Milky Way. 



THE SCALE OF THE UNIVERSE: H. SHAPLE Y A ND H. D. CURTIS 2 13 



This peculiar distribution is admittedly difficult to explain on any 
theory. This factor of distribution in the two theories may be 
contrasted as follows : 



As Island Universes 

It is most improbable that our galaxy 
should, by mere chance, be placed about 
half way between two great groups of 
island universes. 

So many of the edgewise spirals show 
peripheral rings of occulting matter that 
this dark ring may well be the rule rather 
than the exception. 

If our galaxy, itself a spiral on the 
island universe theory, possesses such a 
peripheral ring of occulting matter, this 
would obliterate the distant spirals in our 
galactic plane, and would explain the 
peculiar apparent distribution of the 
spirals. 

There is some evidence for such occult- 
ing matter in our galaxy. 

With regard to the observed excess of 
velocities of recession, additional obser- 
vations may remove this. Part of the 
excess may well be due to the motion of 
our own galaxy in space. The Nebula of 
Andromeda is approaching us. 



As Galactic Phenomena 

If the spirals are galactic objects, they 
must be a class apart from all other 
known types: why none in our neighbor- 
hood? 

Their abhorrence of the regions of 
greatest star density can only be ex- 
plained on the hypothesis that they are, 
in some unknown manner, repelled by 
the stars. 

We know of no force adequate to pro- 
duce such a repulsion, except perhaps 
light-pressure. 

Why should this repulsion have invari- 
ably acted essentially at right angles to 
our galactic plane? 

Why have not some been repelled in 
the direction of our galactic plane? 

The repulsion theory, it is true, is 
given some support by the fact that most 
of the spirals observed to date are reced- 
ing from us. 



The Space velocities oj the spirals. — 



As Island Universes 

The spirals observed to date have the 
enormous average space velocity of 1200 
km/sec. 

In this velocity factor they stand apart 
from all galactic objects. 

Their space velocity is one hundred 
times that of the galactic diffuse nebu- 
losities, about thirty times the average 
velocity of the stars, ten times that of 
the planetary nebulae, and five times that 
of the clusters. 

Such high speeds seem possible for indi- 
vidual galaxies. 

Our own galaxy probably has a space 
velocity, relatively to the system of the 
spirals, of several hundred km/sec. At- 
tempts have been made to derive this 
from the velocities of the spirals, but are 
uncertain as yet, as we have the radial 
velocities of but thirty spirals. 



As Galactic Phenomena 

Space velocities of several hundred 
km/sec. have been found for a few of the 
fainter stars. 

It has been argued that an extension 
of radial velocity surveys to the fainter 
stars would possibly remove the discrep- 
ancy between the velocities of the stars 
and those of the spirals. 

This is possible, but does not seem 
probable. The faint stars thus far se- 
lected for investigation have been stars 
of known large proper motions. They are 
exceptional objects through this method 
of selection, not representative objects. 

High space velocities are the rule, not 
the exception, for thfe spirals. 

High space velocities are still the ex- 
ception, not the rule, for the stars of our 
galaxy. 



2 1 4 THE SCALE OF THE UNI VERSE: H. SHAPLE Y AND H. D. CURTIS 

Proper motions oj ike spirals. — Should the results of the next 
quarter-century show close agreement among different observers to 
the effect that the annual motions of translation or rotation of 
the spirals equal or exceed 0.01 in average value, it would seem 
that the island universe theory must be definitely abandoned. 

A motion of 700 km/sec. across our line of sight will produce 
the following annual proper motions : 

Distance in light-years 1,000 10,000 100,000 1,000,000 
Annual proper motion "48 '.'048 '.'005 '.'0005 

The older visual observations of the spirals have so large a 
probable error as to be useless for the determination of proper 
motions, if small; the available time interval for photographic 
determinations is less than twentyrfive years. 

The first proper motion given above should inevitably have 
been detected by either visual or photographic methods, from 
which it seems clear that the spirals can not be relatively close 
to us at the poles of our flattened galactic disk. In view of the 
hazy character of the condensations measured, I consider the 
trustworthy determination of the second proper motion given 
above impossible by present methods without a much longer 
time interval than is at present available; for the third and the 
fourth, we should need centuries. 

New stars in the spirals. — Within the past few years some 
twenty-seven new stars have appeared in spirals, sixteen of these 
in the Nebula of Andromeda, as against about thirty-five which 
have appeared in our galaxy in the last three centuries. So far 
as can be judged from such faint objects, the novae in spirals have 
a life history similar to that of the galactic novae, suddenly flash- 
ing out, and more slowly, but still relatively rapidly, sinking again 
to a luminosity ten thousand-fold less intense. Such novae form 
a strong argument for the island universe theory and furnish, in 
addition, a method of determining the approximate distances of 
the spirals. 

With all its elements of simplicity and continuity, our universe 
is too haphazard in its details to warrant deductions from small 
numbers of exceptional objects. Where no other correlation is 
available such deductions must be made with caution, and with 
a full appreciation of the uncertainties involved. 

It seems certain, for instance, that the dispersion of the novae 



THE SCA LE OF THE UNI VERSE: H. SHA PLE Y AND H. D. CURTIS 2 1 5 

in the spirals, and probably also in our galaxy, may reach at least 
ten absolute magnitudes, as is evidenced by a comparison of 5 
Andromedae with the faint novae found recently in this spiral. A 
division into two magnitude classes is not impossible. 

Tycho's Nova, to be comparable in absolute magnitude with 
some recent galactic novae, could not have been much more than 
ten light-years distant. If as close to us as one hundred light- 
years it must have been of absolute ma^itude —8 at maximum; 
if only one thousand light-years away, it would have been of abso- 
lute magnitude —13 at maximum. 

The distances and absolute magnitudes of but four galactic 
novae have been thus far determined ; the mean absolute magnitude 
is —3 at maximum, and +7 at minimum. 

These mean values, though admittedly resting upon a very 
limited amount of data, may be compared with the fainter novae 
which have appeared in the Nebula of Andromeda somewhat as 
follows: where 500,000 light-years is assumed for this spiral on 
the island universe hypothesis and, for comparison, the smaller 
distance of 20,000 light-years. 





Apparent magnitudes 




Thirty galactic 
novae 


Sixteen novae in 
Neb. Andromedae 


At maximum 
At minimum 


-t-5 

+ 15± 


+ 17 

+27 (?; conjectured from the analogy 
of the galactic novae) 





Absolute magnitudes 




Four galactic novae 
of known distance 


Sixteen novae in Andr. 
if at distances of, — 


At maximum 
At minimum 


-3 

+ 7 


500,000 1. y. 20,000 1. y. 

-^ +3 

+6? +13? 



It will be seen from the above that, at the greater distance of 
the island universe theory, the agreement in absolute magnitude 
is quite good for the galactic and the spiral novae. If as close as 
20,000 light-3^ears, however, these novae must be unlike similar 
galactic objects, and of unusually low absolute magnitude at 



2 i6 THE SCALE OF THE UNIVERSE: H. SHAPLEY AND H. D. CURTIS 

minimum. Very few stars have thus far been found as low in 
luminosity as absolute magnitude +13, corresponding, at this 
distance, to apparent magnitude 27. 

The simple hypothesis that the novae in spirals represent the running 
down of ordinary galactic stars by the rapidly moving nebulosity becomes 
a possibility on this basis of distance (i. e., 20,000 light-years) for the 
brighter spirals are within the edges of the galactic system (Shapley) . 

This hypothesis of the origin of the novae in spirals is open to 
grave objections. It involves: 

1. That the stars thus overtaken are of smaller absolute lumi- 
nosity than the faintest thus far observed, with very few excep- 
tions. 

2. That these faint stars are extraordinarily numerous, a con- 
clusion which is at variance with the results of star counts, which 
seem to indicate that there is a marked falling off in the number 
of stars below apparent magnitude 19 or 20. 

As an illustration of the difficulties which would attend such a 
hypothesis, I have made a count of the stars in a number of areas 
about the Nebula of Andromeda, including, it is believed, stars 
at least as faint as magnitude 19.5, and find a star density, includ- 
ing all magnitudes, of about 6,000 stars per square degree. 

If no more than 20,000 light-years distant this spiral will lie 
7,000 light-years from the plane of the Milky Way, and if moving 
at the rate of 300 km/sec, it will sweep through 385 cubic light- 
years per year. 

To make the case as favorable as possible for the hypothesis 
suggested, assume that none of the 6,000 stars per square degree 
are as close as 15,000 light-years, but that all are arranged in a 
stratum extending 5,000 light-years each way from the spiral. 

Then the Nebula of Andromeda should encounter one of these 
stars every 520 years. Hence the actual rate at which novae 
have been found in this spiral would indicate a star density about 
two thousand times as great as that shown by the count ; each star 
would occupy about one square second of arc on the photographic 
plate. 

The spirals as island universes: summary. — 

1. On this theory we avoid the almost insuperable difficulties 
involved in an attempt to fit the spirals in any coherent scheme of 
stellar evolution, either as a point of origin, or as an evolutionary 
product. 



THE SCALE OF THE UNIVERSE: H. SHAPLEY AND H. D. CURTIS 217 

2. On this theory it is unnecessary to attempt to coordinate 
the tremendous space velocities of the spirals with those of the 
average star. 

3. The spectrum of the spirals is such as would be expected 
from a galaxy of stars. 

4. A spiral structure has been suggested for our own galaxy, 
and is not improbable. 

5. If island universes, the new stars observed in the spirals 
seem a natural consequence of their nature as galaxies. Corre- 
lations between the novae in the spirals and those in our galaxy 
indicate distances ranging from perhaps 500,000 light-years in 
the case of the Nebula of Andromeda, to 10,000,000 or more light- 
years for the more remote spirals. 

6. At such distances, these island universes would be of the 
same order of size as our own galaxy. 

7. Very many spirals show evidence of peripheral rings of oc- 
culting matter in their equatorial planes. Such a phenomenon 
in our galaxy, regarded as a spiral, would serve to obliterate the 
distant spirals in our galactic plane, and would furnish an adequate 
explanation of the otherwise inexplicable distribution of the 
spirals. 

There is a unity and an internal agreement in the features of 
the island universe theory which appeals very strongly to me. 
The evidence with regard to the dimensions of the galaxy, on 
both sides, is too uncertain as yet to permit of any dogmatic pro- 
nouncements. There are many points of difficulty in either 
theory of galactic dimensions, and it is doubtless true that many 
will prefer to suspend judgment until much additional evidence 
is forthcoming. Until more definite evidence to the contrary is 
available, however, I feel that the evidence for the smaller and 
commonly accepted galactic dimensions is still the stronger; and 
that the postulated diameter of 300,000 light-years must quite 
certainly be divided by five, and perhaps by ten. 

I hold, therefore, to the belief that the galaxy is probably not 
more than 30,000 light-years in diameter; that the spirals are not 
intra-galactic objects but island universes, like our own galaxy, 
and that the spirals, as external galaxies, indicate to us a greater 
universe into which we may penetrate to distances of ten million 
to a hundred million light-years. 



/J .552 



3 5002 00155 0545 

Shapley, Harlow 

The scale of the universe, 



1 





Date Due 





















































































































































AUTHOR 

Sliapley. 


857.7 


TITLE 

' The seal 


e of the universe. 



RSTPONOMV I IRRART 



QB 

857.7 

350- 



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